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arxiv 2005.07570 v2 pith:UXVFXE7L submitted 2020-05-15 hep-lat

Shinichiro Akiyama , Daisuke Kadoh This is my paper · ORCID
classification hep-lat
keywords fermionstensorformulagrassmannstaggeredwilsonfindgroup
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We derive a general formula of the tensor network representation for $d$-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.

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Cited by 5 Pith papers

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  1. Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group

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    hep-lat 2025-01 conditional novelty 6.0 of 10

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  4. Two-color lattice QCD in $(1+1)$ dimensions with Grassmann tensor renormalization group

    hep-lat 2025-01 conditional novelty 5.0 of 10

    Grassmann tensor network simulations of 1+1D two-color lattice QCD reproduce finite-density physics and identify a candidate c=1 critical point for Wilson fermions.

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